An archer is able to hit the bull's eye 74% of the time.If she shoots 130 arrows in a competition,is it appropriate to use a normal model to approximate the distribution of the number of bull's-eyes? Assume that shots are independent of each other.
A)Yes;normal model with μ = 33.8 and σ = 25.01 can be used to approximate the distribution
B)No;normal model cannot be used to approximate the distribution because nq

Question

An archer is able to hit the bull's eye 74% of the time.If she shoots 130 arrows in a competition,is it appropriate to use a normal model to approximate the distribution of the number of bull's-eyes? Assume that shots are independent of each other.
A)Yes;normal model with μ = 33.8 and σ = 25.01 can be used to approximate the distribution
B)No;normal model cannot be used to approximate the distribution because nq < 10
C)Yes;normal model with μ = 96.2 and σ = 5.00 can be used to approximate the distribution
D)No;normal model cannot be used to approximate the distribution because np < 10
E)Yes;normal model with μ = 96.2 and σ = 25.01 can be used to approximate the distribution

Quizplus · Accepted Answer

The normal approximation can be used because both np and nq are greater than 10. Here, np = 130 * 0.74 = 96.2 and nq = 130 * 0.26 = 33.8. The mean μ = np = 96.2 and the standard deviation σ = √(npq) = √(130 * 0.74 * 0.26) ≈ 5.00.

An Archer Is Able to Hit the Bull's Eye 74